L05_rccircuit5

L05_rccircuit5 - RC Circuit Name: Teammates: Introduction...

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RC Circuit Name: Teammates: Introduction All of the circuits that we have studied so far have all been in a steady state, i.e. the current was constant. Circuits in this regime operate on the basis of two things: a constant potential difference to provide a steady stream of electrons and a conducting path. In all of these circuits there is at least one continuous path from positive end of the power supply to the negative end (see Fig 1 for an example.) When like in Fig 2, there is a gap in the circuit there can be no path for the electrons to flow from one end of the battery to the other. In this case, the circuit cannot maintain a steady state. Instead, when the gap is small enough to allow for electrostatic forces to operate across the gap, a non-steady flow of charges in the circuit will occur. The flow will continue until a potential difference equal to the applied potential difference is built across the gap. An example of a small enough gap is the gap present in capacitors. The gap presented by open switch like the one shown in Fig 1 and Fig 2 will not enable any charge flow. The purpose of this lab is to study the non-steady current due to a circuit made up of a capacitor and resistor, often called an RC circuit. Theory An RC circuit consists of a voltage source connected in series with a resistor and a capacitor. Two switches in the circuit allow us to control how currents in the circuit. When switch S1 is closed (Fig 3) with the voltage supply connected, the potential difference as a function of time, V C (t), across an initially uncharged capacitor is given by: E - V C (t) – R i(t) = 0 where i(t) is the time dependent current in the circuit, E is the potential difference provided by the voltage source, R is the resistance in the circuit, C is the capacitance in the circuit, and t is time measured from the instant the switch is closed. . By using differential equation calculus, it can be shown that this leads to: V C (t) = E (1 - e -t / RC ) (Equ. 1) The voltage across the resisto V R (t) is simply given by: V R (t) = E - V C (t) = E (e -t / RC ) Since from Ohm’s law we know that: V R (t) = R i(t) i(t) = V R (t)/R = (E/R) (e -t / RC ) To discharge the capacitor, the voltage source is removed from the circuit, and the charged capacitor is allowed to discharge through the resistor. Fig 4 shows one possible configuration. In this configuration, the voltage across the capacitor as a function of time after discharge is
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L05_rccircuit5 - RC Circuit Name: Teammates: Introduction...

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